In a shallow dish, mix together the flour, salt, black pepper, and cayenne pepper. In a second shallow dish, whisk together the milk and eggs until blended. Spread the cornmeal in a third shallow dish. Have ready a baking sheet.
Core the tomatoes and cut crosswise into slices about ¼-inch thick. One at a time, dip the tomato slices into the flour mixture to coat evenly, shaking off the excess. Dip into the egg mixture, letting the excess drip back into the bowl, and then in the cornmeal, patting gently to help it adhere. Transfer to the baking sheet.
Preheat the oven to 200 degrees. Set a large wire rack on another rimmed baking sheet and place near the stove. In a large frying pan, heat the oil over medium-high heat until it shimmers. In batches to avoid crowding, add the coated tomato slices to the hot oil and cook until the undersides are golden brown, about 2 minutes. Turn the slices and fry until the other sides are browned, about 2 minutes more. Using a slotted spatula, transfer the tomatoes to the rack and keep warm in the oven while you fry the remaining tomatoes. Serve hot, passing the rémoulade on the side.